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Test of lepton universality in beauty-quark decays

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Abstract

The Standard Model of particle physics currently provides our best description of fundamental particles and their interactions. The theory predicts that the different charged leptons, the electron, muon and tau, have identical electroweak interaction strengths. Previous measurements have shown a wide range of particle decays are consistent with this principle of lepton universality. This article presents evidence for the breaking of lepton universality in beauty-quark decays, with a significance of 3.1 standard deviations, based on proton-proton collision data collected with the LHCb detector at CERN's Large Hadron Collider. The measurements are of processes in which a beauty meson transforms into a strange meson with the emission of either an electron and a positron, or a muon and an antimuon. If confirmed by future measurements, this violation of lepton universality would imply physics beyond the Standard Model, such as a new fundamental interaction between quarks and leptons.

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\textcolor{changes}{Contributions to $ B ^+ \rightarrow K ^+ \ell^+ \ell^- $ decays in the SM and possible new physics models.} A $ B ^+ $ meson, consisting of $\overline b $ and $ u $ quarks, decays into a $ K ^+$ , containing $\overline s $ and $ u $ quarks, and two charged leptons, $\ell^+ \ell^- $. (Left) The SM contribution involves the electroweak bosons $\gamma, W^+$ and $Z^0$, \textcolor{changes}{and the up-type quarks $\bar{u}$, $\bar{c}$ and $\bar{t}$}. (Right) A possible new physics contribution to the decay with a hypothetical leptoquark ($LQ$) which, unlike the electroweak bosons, could have different interaction strengths with the different types of leptons.

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Candidate invariant mass distributions. Distribution of the invariant mass $ m_{( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}{( K ^+ \ell^+ \ell^- )}$ for candidates with (left) electron and (right) muon pairs in the final state for the (top) nonresonant $ B ^+ \rightarrow K ^+ \ell^+ \ell^- $ signal channels and (bottom) resonant $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} (\rightarrow \ell^+ \ell^- ) K ^+ $ decays. The fit projection is superimposed\textcolor{changes}{, with dotted lines describing the signal contribution and solid areas representing each of the background components described in the text and listed in the legend}. In the resonant-mode distributions, some fit components are too small to be visible.

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Differential $ r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ measurement. The distributions of (left) the $ B ^+ $ transverse momentum, $ p_{\mathrm{T}}$ , and (right) the ratio $ r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ relative to its average value $\left< r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} } \right>$ as a function of $ p_{\mathrm{T}}$ . The $ p_{\mathrm{T}}$ spectrum of the $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ $ decays is similar to that of the corresponding $ B ^+ \rightarrow K ^+ \ell^+ \ell^- $ decays such that the measurement of $ r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ tests the kinematic region relevant for the $ R_{ K }$ measurement. The lack of any dependence of the value of $ r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} } /\left< r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} } \right>$ as a function of $ B ^+ $ $p_{\mathrm T}$ demonstrates control of the efficiencies. \textcolor{changes}{Uncertainties on the data points are statistical only.}

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Comparison between $ R_{ K }$ measurements. In addition to the LHCb result, the measurements by the BaBar [15] and Belle [13] collaborations, which combine $ B ^+ \rightarrow K ^+ \ell^+ \ell^- $ and $ B ^0 \rightarrow K ^0_{\mathrm{S}} \ell^+ \ell^- $ decays, are also shown. \textcolor{changes}{The vertical dashed line indicates the SM prediction.}

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Simulated $K^+e^-$ mass distributions for signal and various cascade background samples. \textcolor{changes}{The signal is represented by the orange shaded region and the various cascade background contributions by red, dark blue and light blue shaded regions.} The distributions are all normalised to unity. (Left, with log $y$-scale) the bremsstrahlung correction to the momentum of the electron is applied, resulting in a tail to the right. The region to the left of the vertical dashed line is rejected. (Right, with linear $y$-scale) the mass is computed only from the track information. The notation $\pi^-_{[\rightarrow e^-]}$ ($e^-_{[\rightarrow \pi^-]}$) is used to denote an \textcolor{changes}{pion (electron)} that is \textcolor{changes}{reconstructed} as an \textcolor{changes}{electron (pion)}. The region between the dashed vertical lines is rejected.

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Candidate invariant mass distributions. Distribution of the invariant mass $ m({ K ^+ \ell^+ \ell^- })$ for nonresonant candidates in the (left) sample previously analysed [11] and (right) the new data sample. The top row shows the fit to the muon modes and the subsequent rows the fits to the electron modes triggered by (second row) one of the electrons, (third row) the kaon and (last row) by other particles in the event. The fit projections are superimposed\textcolor{changes}{, with dotted lines describing the signal contribution and solid areas representing each of the background components described in the text and listed in the legend}.

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Candidate invariant mass distributions. Distribution of the invariant mass $ m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }{( K ^+ \ell^+ \ell^- )}$ for resonant candidates in the (left) sample previously analysed [11] and (right) the new data sample. The top row shows the fit to the muon modes and the subsequent rows the fits to the electron modes triggered by (second row) one of the electrons, (third row) the kaon and (last row) by other particles in the event. The fit projections are superimposed\textcolor{changes}{, with dotted lines describing the signal contribution and solid areas representing each of the background components described in the text and listed in the legend}.

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\textcolor{changes}{Likelihood function from the fit to the nonresonant $ B ^+ \rightarrow K ^+ \ell^+ \ell^- $ candidates in terms of the ratio between the likelihood value ($L$) and that found by the fit ($L_{\rm max}$) as a function of $ R_{ K }$ .} The extent of the dark, medium and light blue regions shows the values allowed for $ R_{ K }$ at $1\sigma$, $3\sigma$ and $5\sigma$ levels. The red line indicates the prediction from the SM.

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Differential $ r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ measurement. (Top) distributions of the reconstructed spectra of (left) the angle between the leptons\textcolor{changes}{, $\alpha(\ell^+, \ell^-)$}, and (right) the minimum $ p_{\mathrm{T}}$ of the leptons \textcolor{changes}{ for $ B ^+ \rightarrow K ^+ \ell^+ \ell^- $ and $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} (\rightarrow \ell^+ \ell^- ) K ^+ $ decays}. (Bottom) the single ratio $ r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ relative to its average value $\left< r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} } \right>$ as a function of these variables. In the electron minimum $ p_{\mathrm{T}}$ spectra, the structure at 2800 $\text{ Me V /}c$ is related to the trigger threshold. \textcolor{changes}{ Uncertainties on the data points are statistical only.}

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Double differential $ r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ measurement. (Left) the value of $ r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ , relative to the average value of $ r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ , measured in two-dimensional bins of the maximum lepton momentum, $p(\ell)$, and the opening angle between the two leptons, $\alpha(\ell^+,\ell^-)$. (Right) the bin definition in this two-dimensional space together with the distribution for $ B ^+ \rightarrow K ^+ e ^+ e ^- $ ( $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} (\rightarrow e ^+ e ^- ) K ^+ $ ) decays depicted as red (blue) contours. \textcolor{changes}{Uncertainties on the data points are statistical only.}

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Tables and captions

Nonresonant and resonant mode $ q^2 $ and $ m({ K ^+ \ell^+ \ell^- })$ ranges. The variables $ m({ K ^+ \ell^+ \ell^- })$ and $ m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }{( K ^+ \ell^+ \ell^- )}$ are used for nonresonant and resonant decays, respectively.

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Yields of the nonresonant and resonant decay modes obtained from the fits to the data. The quoted uncertainty is the combination of statistical and systematic effects.

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Created on 23 March 2024.